If your phone has "data always" enabled, that is, apps are allowed to send and receive data at any time, then turning WiFi on will save battery life IF you have access to valid WiFi routers.
With access to constant WiFi, the phone will not need to constantly maintain a signal with the cell tower. Obtaining a signal to a cell tower can use more and more power, depending on if the signal is weak.
By using WiFi, in these situations, you relieve your phone from having to step up it's cellular receiver to maintain a data connection, and also, most WiFi connections are able to send and receive more data quickly, so that the time spent sending and receiving data is reduced for any given packet.
So, this depends on your environment and your phone and how it is setup.
